We present a new method for approximate inference in Switching linear Gaussian State Space Models (also known as Switching Kalman Filters. The method is similar in spirit to the Rauch-Tung-Striebel smoother in the Kalman Filter case. Only a single Forward and Backward pass is required, both of which are numerically stable. The algorithm projects at each time, for both the Forward and Backward passes, the approximate Belief states onto either a single or a mixture of Gaussians. Unlike in Expectation Propagation, we find few difficulties with numerical stability.